Summary

This project seeks to improve on the Howard et al. (2020) methods used to estimate sport fish harvest and releases of rockfish in Alaska waters and expand the time series back to 1977 when the statewide harvest survey (SWHS) was first implemented. This is essentially a Bayesian version of the Howard methods that allows for more appropriate and defensible sharing of information between areas, handles missing data in a more appropriate manor, accurately propagates uncertainty throughout the estimation procedure and replaces the Howard decision tree approach to low sample sizes with a hierarchical model. The methods and results for generating harvest estimates are generally consistent between the Bayesian model and the Howard methods. Harvest estimates are consistent with Howard estimates during contemporary times, but may differ based on more appropriate weighting of SWHS and logbook data, including estimating and correcting bias in the SWHS data.

The Bayesian methods depart from the Howard method in how releases are estimated. The Howard methods assume that the species composition of the harvests are equal to the species composition of released fish, which is clearly contraindicated in the logbook data. For instance, logbook data demonstrates that yelloweye have been retained at high levels up until restrictions were enacted in recent years, whereas pelagic rockfish were released in significant numbers in the past with retention increasing in recent years as they have become more prized by anglers. Recent prohibition on retaining yelloweye in Southeast Alaska highlights the the shortcomings of the original Howard methods as the species composition of the harvest would indicate that no yelloweye were caught and released during the closure.

The Howard method for estimating releases for private anglers also relied on an expansion of the logbook release estimates based on the ratio of private:guided releases of all rockfish in the SWHS. In addition to the faulty assumptions about species composition, this method ignores potential bias in SWHS estimates of harvests and releases. As demonstrated below, the bias in those two quantities appears to be quite different based on the logbook data. The Bayesian model thus attempts to estimate release probabilities based on the logbook data coupled with bias corrected estimates from the SWHS.

Lastly, the Howard methods were only used on data beginning in 1999 with the advent of the logbook program and estimates of harvests and releases prior to that have been based on linear ramps from 1999 back to the perceived start of the fishery. The Bayesian methods allow us to expand the time series back to 1977 when the SWHS was implemented by leveraging regional data trends in species composition and the proportion of caught rockfish harvested by species and/or species complex. Key advantages of the Bayesian approach are highlighted in table 1.

Table 1. Summary of key improvements in reconstructiing sport fish removals of rockfish using the Bayesian model as compared to the Howard et al. (2020) methods.
Issue Howard Bayes
Time series 1999 - present 1977 - present
Bias in SWHS Not explicitly dealt with. Relies on logbook data and ratios of guided/unguided from SWHS data to estimate unguided releases and harvests. Explicitly estimates bias in SWHS harvest and release estimates based on logbook data.
Species composition of releases Assumes that species composition of releases is equal to that of the harvest, which is not evident in the logbook data. Recognizes different release probabilities by species / species assemblage and estimates it from logbook data and bias corrected SWHS data
Sample size limitations Uses sample size threshholds such that when areas fall below those threshholds values are borrowed from nearby areas. Uses a hierarchichacal modelling approach that shares information between areas in the same region. Thus all data is used, even with small sample sizes. This is a more sound method that avoids assumptions and uses all of the data.
Error propogation Error is propogated when variance estimates are available, but there is uncertainty associated with borrowing values from nearby areas, or the assumption of species compositions being identical in harvest and releases, are not dealt with. By breaking the assumption that species composition is equal between harvests and releases, uncertainty in the release estimates is more reflective of the fishery. Furthermore, the hyerarchichal approach more accurately captures uncertainy within and between areas within a region.

Data

Harvest data was available for 22 commercial fishing management areas in Southcentral and Southeast Alaska. Areas with negligible rockfish harvest were pooled with adjacent areas for analysis. Specifically the Aleutian and Bering areas were pooled into an area labeled BSAI; the IBS and EKYT were pooled into an area labeled EKYKT; the Southeast, Southwest, SAKPEN and Chignik areas were pooled into an area labeled SOKO2PEN and the Westside and Mainland areas were pooled into an area labeled WKMA.

Stateside Harvest Survey (SWHS)

Statewide harvest survey estimates of rockfish catch and harvest are available for 28 years (1996-2023) for all users and for 13 years (2011-2023) for guided anglers (Figure 0). Additionally, there are overall harvest estimates from 1977- 1995 and release estimates from 1990-1995 that required some partitioning to ascribe to current management units. Harvests in unknown areas were apportioned based on harvest proportions in 1996. Variance estimates are not available for pre-1996 data and as such, the maximum observed coefficient of variation (cv) in each commercial fisheries management unit was applied to the pre-1996 values.

**Figure 0.**- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units.

Figure 0.- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units.


SWHS estimates are believed to be biased to some degree. These modelling efforts aim to estimate and correct for that bias with the assumption that logbook records are a census of guided harvests and releases.

SWHS Rockfish release estimates are inferred from the difference between catch and harvest estimates.

Adam noted that the first 5 years (23 years counting the historical data) in the SWHS data set for PWSO seem unreasonable (close to zero and not corroborated with logbook estimates). Adam recommended setting these harvests to unknown, but current model development has included the data. Once a satisfactory model has been identified we will exam the effects of censoring the PWSO data.

Creel Surveys

NA

Guide Logbooks

Sport fishing guides have been required to report their harvest of rockfish for 26 years (1998-2023). Reported harvest is also available by assemblage (pelagic vs. non-pelagic). Harvest of yelloweye and “other” (non-pelagic, non-yelloweye) rockfish were reported separately beginning in 2006.

Logbooks also record the number of rockfish released for the same categories. However, the reliability of the release data is somewhat questionable as reported releases are generally far lower than that estimated by the SWHS. As such several treatments of the data are considered.

Logbook versus SWHS estimates

Estimates of guided harvests and releases from the SWHS do not align with the census from charter logbooks. Logbook harvest reports are generally considered reliable and are used to assess the bias in SWHS reports. However, there is even greater disparity between release estimates in the two sources and it is debatable whether logbook releases should be treated as a census. The Howard et al. (2020) methods do treat the logbook release data as “true” and thus are considerably less than would be estimated from the SWHS data.

**Figure 1.**- SWHS harvest (left) and release (right) estimates from guided trips (x-axis) versus repoted harvests from charter logbooks (y-axis).

Figure 1.- SWHS harvest (left) and release (right) estimates from guided trips (x-axis) versus repoted harvests from charter logbooks (y-axis).


A note on model development

To evaluate the discrepancy in apparent bias in harvest and release data, several models were explored to estimate releases during model development. One method (\(LB_{fit}\)) considers the logbook release data to be reliable and a second method (\(LB_{cens}\)) treated the logbook release data as estimates of the minimum released, thus giving more weight to SWHS release estimates. A third method (\(LB_{hyb}\)) is a hybrid approach that treats reported releases of yelloweye as reliable but total rockfish and pelagic rockfish releases as minimums. Model development revealed a tension between the total and pelagic logbook releases and the yelloweye logbook releases. This tensions eventually highlighted the different release/retention probabilities between yelloweye and pelagics in the logbook data and prompted the current approach whereby that probability was calculated for the three main species complexes covered in the data: pelagics, yelloweye, and “other”. The methods described here follow the (\(LB_{fit}\)) formulation. Based on model behavior it is unlikely that the (\(LB_{cens}\)) model would work as there would not be enough data to estimate release probabilities. However, it may be worth running the (\(LB_{hyb}\)) approach as a sensitivity test at the very least.

Composition data

Harvest sampling data exists from Gulf of Alaska areas since 1996 and from Southeast Alaska areas since 2006. Port sampling data is comprised of the number of total rockfish, pelagic and non-pelagic rockfish, black rockfish and yelloweye rockfish. In Southeast Alaska, the number of Demersal Shelf Rockfish (DSR, of which yelloweye are one species) and slope rockfish are also recorded.

Process equations

The true harvest \(H_{ay}\) of rockfish for area \(a\) during year \(y\) is assumed to follow a temporal trend defined by a penalized spline:

\[\begin{equation} \textrm{log}(H_{ay})~\sim~\textrm{Normal}(f(a,y), {\sigma_H}) \end{equation}\]

where \(f(a,y)\) in a p-spline basis with 7 components (knots) and a second degree penalty. The variance, \(\sigma_H\), was given a normal prior with a mean and standard deviation of 0.25 and 1, respectively.

Charter and private harvest \(H_{ayu}\) (where u = 1 for charter anglers and u = 2 for private anglers) is a fraction of total annual harvest in each area:

\[\begin{equation} H_{ay1}~=~H_{ay}P_{(user)ay1}\\H_{ay2}~=~H_{ay}(1-P_{(user)ay1}) \end{equation}\]

where \(P_{(user)ay1}\) is the fraction of the annual harvest in each area taken by charter anglers. \(P_{(user)ay1}\) was modeled hierarchically across years as:

\[\begin{equation} P_{(user)ay1}~\sim~\textrm{beta}(\lambda1_a, \lambda2_a) \end{equation}\]

with non-informative priors on both parameters.

Annual black rockfish harvest \(H_{(black)ayu}\) for each area and user group is:

\[\begin{equation} H_{(black)ayu}~=~H_{ayu}P_{(pelagic)ayu}P_{(black|pelagic)ayu} \end{equation}\]

where \(P_{(pelagic)ayu}\) is the fraction of the annual harvest for each area and user group that was pelagic rockfish and \(P_{(black|pelagic)ayu}\) is the fraction of the annual harvest of pelagic rockfish for each area and user group that was black rockfish.

The southeast region also tracks two other non-pelagic rockfish assemblages, demersal shelf rockfish (DSR, which includes yelloweye) and slope rockfish. For the southeast region the harvest of those two assemblages is thus

\[\begin{equation} H_{(DSR)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(DSR|non-pelagic)ayu}\\ H_{(slope)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(slope|non-pelagic)ayu}\\ \end{equation}\]

where \(P_{(DSR|non-pelagic)ayu}\) and \(P_{(slope|non-pelagic)ayu}\) are the fractions of the annual harvest of non-pelagic rockfish for each area and user group that were DSR and slope rockfish, respectively.

Annual yelloweye rockfish harvest \(H_{(yelloweye)ayu}\) for each area and user group is calculated differently for central/Kodiak areas and southeast areas. For central and Kodiak areas yelloweye rockfish harvests are calculated as

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(yelloweye|non-pelagic)ayu} \end{equation}\]

where \(P_{(yellow|non-pelagic)ayu}\) is the fraction of the annual harvest of non-pelagic rockfish for each area and user group that was yelloweye rockfish.

For southeast areas yelloweye harvests are a fraction of the DSR harvests such that

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{(DSR)ayu}P_{(yelloweye|DSR)ayu} \end{equation}\]

The composition parameters \(P_{(comp)ayu}\), were modeled using a logistic curve that would allow hindcasting without extrapolating beyond the limit of observed values such that:

\[\begin{equation} \textrm{logit}(P_{(comp)ayu})~=~\beta0_{(comp)ayu} + \frac{\beta1_{(comp)ayu}}{(1 + exp(\beta2_{(comp)ayu}*(y - \beta3_{(comp)ayu})))} + \beta4_{(comp)ayu}*I(u=private)+re_{(comp)ayu} \end{equation}\]

where the \(\beta\) parameters define the intercept, scaling factor, slope, inflection point and private angler effect, respectively, \(y\) is the year index, \(I(u=private)\) is an index variable which is 1 when the user groups is private and 0 otherwise and \(re_{(comp)ayu}\) is a random effect with a non-informative prior. \(\beta\) parameters were modeled hierarchically by region. When \(\beta\) parameters were inestimable as a result of no discernible change in composition over the observed time period. \(\beta1\) (scaling factor) and \(\beta2\) (slope) were fixed to 0 so that the long term mean value was used for hindcasting.

The true number of released rockfish \(R_{ayu}\) were based on the proportion of the total catch harvested, \(pH_{(comp)ayu}\), by area, year, user group and species grouping. Because release data from the SWHS is for all rockfish and the release data from logbooks is only subdivided into pelagics, yelloweye and “other” (non-pelagic, non-yelloweye), we only estimated \(pH_{(comp)ayu}\) for those categories. Thus, converting \(H_{(comp)ayu}\) to total catches by user group, \(C_{(comp)ayu}\), with \(pH_{(comp)ayu}\) results in estimates of total releases such that

\[\begin{equation} R_{(comp)ayu}~=~ C_{(comp)ayu} - H_{(comp)ayu} ~=~ \frac{H_{(comp)ayu}}{pH_{(comp)ayu}} - H_{(comp)ayu} \end{equation}\]

with total releases equal to the sum of the compositional releases. For non-yelloweye DSR and Slope rockfish assemblages in Southeast Alaska \(R_{(DSR)ayu}\) and \(R_{(slope)ayu}\) were estimated from \(R_{(other)ayu}\) using the species composition data from the harvest, thus assuming that slope and DSR assemblages were caught and released at the same rates.

The proportion harvest parameters for \(pH_{(comp)ayu}\) were modeled using a logistic curve that would allow hindcasting based on trends in the data without extrapolating beyond the range of observed values such that

\[\begin{equation} \textrm{logit}(pH_{(pH)ayuc})~=~\beta0_{(pH)ayu} + \frac{\beta1_{(pH)ayuc}}{(1 + exp(\beta2_{(pH)ayuc}*(y - \beta3_{(pH)ayuc})))} + \beta4_{(pH)ayuc}*I(u=private)+re_{(pH)ayuc} \end{equation}\]

A random effect term allowed estimation during the historical period when data is available, but the curve defined by the above equation determined release estimates between 1977 and 1990. As with the compositional trends, \(\beta\) parameters were modeled hierarchically by region. When \(\beta\) parameters were inestimable as a result of no discernable change in harvest probability over the observed time period, \(\beta1\) (scaling factor) and \(\beta2\) (slope) were fixed to 0 so that the long term mean value was applied.

Observation equations

SWHS estimates of annual rockfish harvest \(\widehat{SWHS}_H{ay}\) were assumed to index true harvest:

\[\begin{equation} \widehat{SWHS}_H{ay}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay}b_{ay}), \sigma_{SWHSHay}^2\right) \end{equation}\]

where bias in the SWHS harvest estimates \(b_H{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_H{ay}~\sim~\textrm{Normal}(\mu_H{(b)a}, \sigma_H{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

SWHS estimates of guided angler harvest \(\widehat{SWHS}_H{ay1}\) are related to total harvest by:

\[\begin{equation} \widehat{SWHS}_H{ay1}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay1}b_{ay}), \sigma_{SWHS_{ay1}}^2\right) \end{equation}\]

Reported guide logbook harvest \(\widehat{LB}_H{ay}\) is related to true harvest as:

\[\begin{equation} \widehat{LB}_H{ay}~\sim~\textrm{Poisson}(H_{ay1})\\ \widehat{LB}_H{(pelagic)ay}~\sim~\textrm{Poisson}(H_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_H{(yelloweye)ay}~\sim~\textrm{Poisson}(H_{(yelloweye)ay1})\\ \widehat{LB}_H{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(H_{(nonpel,nonye)ay1})\\ \end{equation}\]

Note that for central and Kodiak areas \(H_{(nonpel,nonye)ay1}\) is equal to the total harvest minus pelagic and yelloweye harvests. For southeast areas \(H_{(nonpel,nonye)ay1}\) is equal to the sum of the DSR and slope harvests minus yelloweye harvests.

SWHS estimates of annual rockfish releases \(\widehat{SWHS}_R{ay}\) were assumed to index true releases in a similar fashion and thus modeled similarly. As such, the release data are related to true releases just as harvests were modeled such that:

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{Poisson}(R_{ay1})\\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{Poisson}(R_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Because logbook release data is more questionable and demonstrates greater disagreement with SWHS estimates (Figure 1), a second approaches was considered that loosened the assumption that logbook releases were a census. Results for this approach are not included in this document, but the methods are listed here for future reference and consideration. In a hybrid approach yelloweye and non-pelagic releases are regarded as a reliable census (given the emphasis and ease of recording these fish) but censors the pelagic and total rockfish release estimates such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

SWHS estimates of guided angler release \(\widehat{SWHS}_R{ay1}\) is modeled the same as harvests.

SWHS release bias was modeled independently of the harvest bias \(b_H{ay}\) such that

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

where bias in the SWHS release estimates \(b_R{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

The number of pelagic rockfish sampled in harvest sampling programs \(x_{(pelagic)ayu}\) follow a binomial distribution:

\[\begin{equation} x_{(pelagic)ayu}~\sim~\textrm{Binomial}(P_{(pelagic)ayu}, N_{ayu}) \end{equation}\]

where \(N_{ayu}\) is the total number of rockfish sampled in area \(a\) during year \(y\) form user group \(u\). The number of black rockfish sampled in harvest sampling programs was thus a proportion of the pelagic harvests

\[\begin{equation} x_{(black)ayu}~\sim~\textrm{Binomial}(P_{(black)ayu}, N_{ayu}^{pel}) \end{equation}\]

Yelloweye rockfish in Southcentral and Kodiak were modeled similarly as a proportion of the total number of non-pelagics such that

\[\begin{equation} x_{(yellow_{R2})ayu}~\sim~\textrm{Binomial}(P_{(yellow_{R2})ayu}, N_{ayu}^{nonpel}) \end{equation}\]

Southeast areas have several other non-pelagic groupings such that DSR and slope rockfish are a proportion of non-pelagics

\[\begin{equation} x_{(DSR)ayu}~\sim~\textrm{Binomial}(P_{(DSR)ayu}, N_{ayu}^{nonpel}) \end{equation}\]

and

\[\begin{equation} x_{(slope)ayu}~\sim~\textrm{Binomial}(P_{(slope)ayu}, N_{ayu}^{nonpel}) \end{equation}\]

with yelloweye in southeast a proportion of the DSR harvest

\[\begin{equation} x_{(yellow_{R1})ayu}~\sim~\textrm{Binomial}(P_{(yellow_{R1})ayu}, N_{ayu}^{DSR}) \end{equation}\].

Priors.

Priors range from uninformative to very informative or fixed. Priors for compositional logistic parameters are in Table 2 and proportion harvest logistic parameters are in Table 3. Until I figure out how to make a nice table in Rmarkdown, please refer to the attached spreadsheet and comp and harvp tabs.

Unresolved issues and outstanding questions:

  1. Reliability of unguided release estimates: These estimates have the least information feeding them and rely on the bias-corrected SWHS release estimates of all rockfish and the trends in release probability evident in the logbook data. The $ term that estimates the guided/unguided effect was given a very informative prior that tied the release probability of private anglers tightly to that of the charter fleet. The model is then trying to balance the three species complex estimates (pelagic, yelloweye and other) so that they sum to the total unguided releases estimated from the bias corrected SWHS data. For the most part this seems reasonable and appears to work, but there are certain areas where the estimates are “wonky”. Yelloweye releases in the Kodiak Northeast area in particular are significantly lower than for guided anglers with the same pattern evident in Cook Inlet to a lesser extent. Cook Inlet yelloweye numbers are very small, so this is a sample size issue with little consequence. The cause of the Kodiak northeast estimates is not clear to me at this point, but it must be a product of the bias corrected SWHS release estimates and how the model is divying up that estimate into the 3 species complexes. The results are also substantially different from the Howard methods and are much lower for black rockfish while disagreements for yelloweye are in both directions. Total rockfish releases more or less align with the total releases estimated with the Howard methods. Presumably, much of the discrepancy results from the substantial bias in release estimates from the SWHS. Interestingly, the logbook data indicates that the SWHS underestimates harvests but overestimates releases.

  2. Proportion guided estimates: There is not much data on this proportion prior to 2011 and it is not modeled with any sort of trend as was done for species composition and harvest proportions. With the exception of Cook Inlet and North Gulf Coast areas, there is little, if any, trend apparent in the data and perhaps this approach is the best available given the data available. However, if there are data sources somewhere that could inform this part of the model they could be incorporated.

  3. Prior choices in general need to be vetted. The priors on the logistic curves are fairly informed in an effort to achieve the desired shapes for hindcasting. Ideally, sensitivity testing would occur but the model is very slow to converge. The beta parameters on the logistic curves have required a lot of work on the priors to reach convergence.

Results

**Figure X.**- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Figure X.- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Estimate comparison

Since previous estimates of rockfish harvest have been produced these first 3 graphs will be used to show how the modeled estimates compare to the estimates produced earlier. For total rockfish the estimates are in general agreement although differences are noted. These estimates should be more reliable because they include both SWHS and guide logbook data, handle variance more appropriately, use hierarchical distributions when data is missing, directly consider observation error and are produced using reproducible research.

**Figure 2.**- Total rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 2.- Total rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 3.**- Total rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 3.- Total rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


Notes from Adam: When looking at only black rockfish the most significant differences are for the Prince William Sound Inside area. I did not spend a great deal of time tracking this down although it looks like the previous version used bad values for \(P_{(black)ayu}\) for at least unguided anglers. For the moment I would ignore the results for BSIA and SOKO2SAP. I think it is possible to give approximate values for these areas but it will require a little more coding which I have yet to do.

**Figure 4.**- Black rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 4.- Black rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


And black rockfish releases…

**Figure 5.**- Black rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 5.- Black rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- Yellow rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Yellow rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- Yellow rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Yellow rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 8.**- DSR rockfish (including yelloweye) harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 8.- DSR rockfish (including yelloweye) harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 9.**- DSR rockfish releases (including yelloweye) 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 9.- DSR rockfish releases (including yelloweye) 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 10.**- Slope rockfish harvests 1996-2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 10.- Slope rockfish harvests 1996-2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 11.**- Slope rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 11.- Slope rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Model fit

Logbook residuals

**Figure 12.**- Residuals from logbook harvests

Figure 12.- Residuals from logbook harvests


SWHS residuals

**Figure 13.**- Residuals from SWHS harvests.

Figure 13.- Residuals from SWHS harvests.



**Figure 14.**- Residual of SWHS releases

Figure 14.- Residual of SWHS releases

Parameter estimates

P(Charter)

These histograms show the posterior distribution of the mean percent of rockfish harvested by the charter fleet.

**Figure 15.**- Mean percent of harvest by charter anglers.

Figure 15.- Mean percent of harvest by charter anglers.


When considered annually we see the percent of rockfish harvested by the charter fleet follows our data fairly well although the model smooths out the changes and we just do not have much information about this ratio. Prior to 2011 the percent charter is confounded with SWHS bias and should be mostly discounted.

**Figure 16.**- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

Figure 16.- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

P(Harvest)

These plots show the fitted logistic line to the proportion of caught rockfish that are harvested. These estimates are used for hindcasting catch estimates based on the harvest data in early years when catch estimates are unavailable.


**Figure 18.**- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 18.- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 19.**- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 19.- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 20.**- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.

Figure 20.- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.


## NULL


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SWHS bias

Figure 23 shows the mean estimate for SWHS bias in harvests and releases. Cook Inlet, North Gulf Coast and North Southeast Inside all look pretty good while most other areas have substantial bias. Prince William Sound Inside has the largest bias. Bias in release estimates is substantial and whereas the SWHS appears to underestimate harvests, it appears to greatly overestimates releases by a factor of 2 or more in most areas as derived from logbook reported releases.

**Figure 23.**- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 23.- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.


Our estimates of SWHS harvest bias track observations fairly well when he have guided harvest estimates. The estimates of release bias in the SWHS data track observed patterns to an extent, but appear to smooth these more volatile disagreements with the logbook data. Adam postulated in his initial start on this that some of this could be the result of the estimates of the proportion guided. This value was not modelled with a trend and thus applies a constant estimate when hindcasting. Data on these relationships could greatly improve this model.

**Figure 24.**- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 24.- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.

P(pelagic)

We model the percentage of pelagic rockfish in the harvest because we have the information for charter anglers (via logbooks) starting in 1998. Other than looking at the model estimates you can use Figure 25 to compare the two data streams for pelagic rockfish harvest. In general they are in agreement with major exceptions in Price William Sound inside, Prince William Sound outside (early in the time series) and South Southeast inside.

**Figure 25.**- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 25.- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(black|pelagic)

Note that in Southeast Alaska we only have composition data starting in 2006. Tania dug up old SE data, but it did not provide any useful data for species apportionment. For the most part, P(black|pelagic) is relatively constant across areas, with the exception of Cook Inlet and NSEI in Southeast AK. It may be worth discussing whether the shifts in those areas is a result of improved or changing species identification rather than actual shift in the species composition of the catch.

**Figure 26.**- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 26.- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(yelloweye|non-pelagic / yelloweye|DSR)

**Figure 27.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 27.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

P(DSR|non-pelagic)

**Figure 28.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

Figure 28.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

P(slope|non-pelagic)

**Figure 30.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 30.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.



P(slope|non-pelagic & non-yellowye) For release estimates

**Figure 31.**- Annual estimates of the percent of the sport non-pelagic, non-yelloweye releases that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023.

Figure 31.- Annual estimates of the percent of the sport non-pelagic, non-yelloweye releases that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023.



Summary of unconverged parameters:

Table 1. Summary of unconverged parameters including the number (n) and the average Rhat from the unconverged parameters.
parameter n badRhat_avg
beta0_pH 1 1.814014
beta1_pelagic 4 1.609936
beta3_pH 1 1.553331
beta0_pelagic 4 1.461267
beta1_pH 4 1.383569
beta2_yellow 4 1.319049
tau_beta0_pH 1 1.281930
beta2_pelagic 3 1.273891
parameter n badRhat_avg
beta1_black 1 1.267174
beta2_pH 1 1.264735
beta1_yellow 1 1.236576
beta3_black 1 1.219084
beta3_yellow 1 1.146369
tau_beta0_black 1 1.125448
mu_beta0_pH 1 1.113630
Table 2. Summary of unconverged parameters by area
CI CSEO NG NSEI NSEO PWSI PWSO SOKO2SAP SSEO
beta0_pelagic 0 1 0 0 0 1 1 0 1
beta0_pH 1 0 0 0 0 0 0 0 0
beta1_black 0 0 0 1 0 0 0 0 0
beta1_pelagic 0 1 0 0 0 1 1 0 1
beta1_pH 1 0 0 0 0 1 1 1 0
beta1_yellow 1 0 0 0 0 0 0 0 0
beta2_pelagic 0 0 0 1 0 1 1 0 0
beta2_pH 1 0 0 0 0 0 0 0 0
beta2_yellow 1 0 1 0 0 1 1 0 0
beta3_black 0 0 0 1 0 0 0 0 0
beta3_pH 1 0 0 0 0 0 0 0 0
beta3_yellow 0 0 0 0 1 0 0 0 0
mu_beta0_pH 1 0 0 0 0 0 0 0 0
tau_beta0_black 0 0 1 0 0 0 0 0 0
tau_beta0_pH 1 0 0 0 0 0 0 0 0

Parameter estimates:

Summary Table of Parameter Estimates
Parameter mean sd Lower_CI Median Upper_CI
mu_bc_H[1] -0.128 0.074 -0.264 -0.132 0.029
mu_bc_H[2] -0.094 0.046 -0.173 -0.096 0.004
mu_bc_H[3] -0.437 0.070 -0.567 -0.439 -0.289
mu_bc_H[4] -0.985 0.192 -1.378 -0.986 -0.619
mu_bc_H[5] 0.929 0.928 -0.155 0.732 3.267
mu_bc_H[6] -2.175 0.318 -2.788 -2.178 -1.523
mu_bc_H[7] -0.457 0.110 -0.673 -0.457 -0.247
mu_bc_H[8] 0.251 0.364 -0.332 0.211 1.030
mu_bc_H[9] -0.292 0.136 -0.560 -0.292 -0.020
mu_bc_H[10] -0.107 0.069 -0.236 -0.110 0.035
mu_bc_H[11] -0.122 0.038 -0.197 -0.123 -0.047
mu_bc_H[12] -0.255 0.107 -0.492 -0.251 -0.051
mu_bc_H[13] -0.135 0.077 -0.280 -0.136 0.017
mu_bc_H[14] -0.299 0.095 -0.490 -0.298 -0.125
mu_bc_H[15] -0.342 0.050 -0.438 -0.343 -0.243
mu_bc_H[16] -0.259 0.395 -0.930 -0.303 0.608
mu_bc_R[1] 1.348 0.145 1.059 1.347 1.636
mu_bc_R[2] 1.454 0.093 1.272 1.454 1.638
mu_bc_R[3] 1.402 0.143 1.114 1.401 1.689
mu_bc_R[4] 0.893 0.207 0.460 0.905 1.275
mu_bc_R[5] 1.144 0.466 0.238 1.141 2.053
mu_bc_R[6] -1.584 0.428 -2.428 -1.583 -0.755
mu_bc_R[7] 0.451 0.213 0.020 0.460 0.841
mu_bc_R[8] 0.557 0.195 0.161 0.566 0.909
mu_bc_R[9] 0.339 0.205 -0.098 0.350 0.697
mu_bc_R[10] 1.296 0.136 1.024 1.298 1.547
mu_bc_R[11] 1.037 0.097 0.846 1.038 1.232
mu_bc_R[12] 0.824 0.204 0.409 0.827 1.228
mu_bc_R[13] 1.029 0.102 0.822 1.029 1.230
mu_bc_R[14] 0.896 0.143 0.613 0.898 1.182
mu_bc_R[15] 0.784 0.108 0.577 0.782 1.004
mu_bc_R[16] 1.098 0.129 0.839 1.098 1.352
tau_pH[1] 5.169 0.449 4.319 5.160 6.082
tau_pH[2] 2.011 0.224 1.590 2.000 2.480
tau_pH[3] 2.005 0.264 1.537 1.993 2.557
beta0_pH[1,1] 0.539 0.176 0.172 0.547 0.873
beta0_pH[2,1] 1.367 0.186 0.993 1.377 1.703
beta0_pH[3,1] 1.428 0.198 0.978 1.444 1.767
beta0_pH[4,1] 1.588 0.214 1.123 1.606 1.957
beta0_pH[5,1] -0.883 0.292 -1.526 -0.861 -0.388
beta0_pH[6,1] -0.726 0.499 -2.038 -0.638 -0.058
beta0_pH[7,1] -0.580 0.475 -1.780 -0.537 0.257
beta0_pH[8,1] -0.668 0.286 -1.298 -0.642 -0.193
beta0_pH[9,1] -0.661 0.283 -1.317 -0.641 -0.169
beta0_pH[10,1] 0.229 0.205 -0.193 0.240 0.610
beta0_pH[11,1] -0.054 0.164 -0.383 -0.049 0.261
beta0_pH[12,1] 0.481 0.190 0.109 0.479 0.858
beta0_pH[13,1] 0.006 0.147 -0.290 0.010 0.299
beta0_pH[14,1] -0.304 0.164 -0.631 -0.298 0.021
beta0_pH[15,1] -0.043 0.183 -0.431 -0.033 0.287
beta0_pH[16,1] -0.442 0.358 -1.304 -0.382 0.098
beta0_pH[1,2] 2.816 0.164 2.474 2.822 3.114
beta0_pH[2,2] 2.883 0.134 2.606 2.884 3.147
beta0_pH[3,2] 3.121 0.172 2.802 3.125 3.443
beta0_pH[4,2] 2.940 0.137 2.673 2.938 3.210
beta0_pH[5,2] 4.815 1.429 3.003 4.509 8.507
beta0_pH[6,2] 3.123 0.208 2.695 3.127 3.524
beta0_pH[7,2] 1.853 0.191 1.469 1.862 2.217
beta0_pH[8,2] 2.877 0.175 2.540 2.875 3.225
beta0_pH[9,2] 3.436 0.216 3.024 3.438 3.860
beta0_pH[10,2] 3.747 0.197 3.361 3.751 4.132
beta0_pH[11,2] -4.818 0.301 -5.418 -4.817 -4.234
beta0_pH[12,2] -4.766 0.395 -5.553 -4.766 -4.022
beta0_pH[13,2] -4.570 0.395 -5.315 -4.586 -3.759
beta0_pH[14,2] -5.557 0.474 -6.567 -5.545 -4.696
beta0_pH[15,2] -4.296 0.351 -4.958 -4.306 -3.589
beta0_pH[16,2] -4.859 0.379 -5.655 -4.850 -4.112
beta0_pH[1,3] 0.840 1.226 -1.930 0.855 2.198
beta0_pH[2,3] 2.199 0.168 1.868 2.200 2.525
beta0_pH[3,3] 2.524 0.154 2.224 2.523 2.828
beta0_pH[4,3] 2.954 0.170 2.629 2.952 3.288
beta0_pH[5,3] 1.140 1.395 -0.854 0.872 4.696
beta0_pH[6,3] -0.323 0.924 -1.898 -0.455 1.492
beta0_pH[7,3] 0.590 0.173 0.253 0.592 0.926
beta0_pH[8,3] 0.298 0.194 -0.094 0.300 0.680
beta0_pH[9,3] -0.681 0.489 -2.117 -0.614 0.028
beta0_pH[10,3] 0.442 0.366 -0.465 0.480 1.048
beta0_pH[11,3] -0.157 0.346 -0.828 -0.149 0.498
beta0_pH[12,3] -0.822 0.358 -1.591 -0.793 -0.183
beta0_pH[13,3] -0.143 0.319 -0.789 -0.144 0.463
beta0_pH[14,3] -0.271 0.271 -0.809 -0.275 0.250
beta0_pH[15,3] -0.681 0.300 -1.270 -0.675 -0.095
beta0_pH[16,3] -0.385 0.292 -0.969 -0.386 0.190
beta1_pH[1,1] 3.089 0.328 2.502 3.069 3.798
beta1_pH[2,1] 2.148 0.284 1.668 2.129 2.793
beta1_pH[3,1] 1.978 0.316 1.464 1.953 2.696
beta1_pH[4,1] 2.385 0.417 1.828 2.330 3.227
beta1_pH[5,1] 2.328 0.374 1.728 2.289 3.257
beta1_pH[6,1] 3.893 1.135 2.364 3.661 6.748
beta1_pH[7,1] 2.746 0.954 1.073 2.654 5.175
beta1_pH[8,1] 3.999 0.962 2.614 3.812 6.328
beta1_pH[9,1] 2.360 0.405 1.713 2.314 3.290
beta1_pH[10,1] 2.401 0.285 1.891 2.388 3.006
beta1_pH[11,1] 3.233 0.212 2.824 3.231 3.656
beta1_pH[12,1] 2.555 0.222 2.119 2.557 2.988
beta1_pH[13,1] 2.968 0.211 2.569 2.960 3.394
beta1_pH[14,1] 3.406 0.215 3.001 3.403 3.846
beta1_pH[15,1] 2.545 0.229 2.113 2.542 3.027
beta1_pH[16,1] 4.065 0.645 3.140 3.959 5.698
beta1_pH[1,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[2,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[3,2] 0.020 0.147 0.000 0.000 0.012
beta1_pH[4,2] 0.006 0.079 0.000 0.000 0.003
beta1_pH[5,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[6,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[7,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[8,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[9,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[10,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[11,2] 6.649 0.334 5.983 6.650 7.301
beta1_pH[12,2] 6.427 0.459 5.565 6.413 7.352
beta1_pH[13,2] 6.950 0.436 6.101 6.951 7.775
beta1_pH[14,2] 7.205 0.491 6.318 7.186 8.231
beta1_pH[15,2] 6.782 0.375 6.027 6.787 7.500
beta1_pH[16,2] 7.452 0.418 6.611 7.448 8.289
beta1_pH[1,3] 2.394 2.681 0.000 2.383 8.361
beta1_pH[2,3] 0.000 0.000 0.000 0.000 0.000
beta1_pH[3,3] 0.000 0.000 0.000 0.000 0.000
beta1_pH[4,3] 0.000 0.000 0.000 0.000 0.000
beta1_pH[5,3] 3.891 4.494 1.448 2.991 12.709
beta1_pH[6,3] 2.551 2.698 0.734 2.389 4.648
beta1_pH[7,3] 0.000 0.000 0.000 0.000 0.000
beta1_pH[8,3] 2.748 0.358 2.070 2.748 3.449
beta1_pH[9,3] 2.790 0.506 1.973 2.735 4.103
beta1_pH[10,3] 2.927 0.440 2.209 2.884 3.984
beta1_pH[11,3] 2.741 0.396 1.993 2.729 3.534
beta1_pH[12,3] 4.067 0.462 3.165 4.052 5.012
beta1_pH[13,3] 1.725 0.339 1.080 1.731 2.404
beta1_pH[14,3] 2.517 0.349 1.834 2.509 3.221
beta1_pH[15,3] 1.966 0.333 1.315 1.970 2.614
beta1_pH[16,3] 1.791 0.330 1.126 1.793 2.425
beta2_pH[1,1] 0.476 0.122 0.287 0.458 0.758
beta2_pH[2,1] 0.596 0.375 0.248 0.524 1.332
beta2_pH[3,1] 0.664 0.455 0.221 0.553 1.841
beta2_pH[4,1] 0.490 0.230 0.204 0.447 1.010
beta2_pH[5,1] 1.380 0.980 0.211 1.226 3.722
beta2_pH[6,1] 0.182 0.063 0.084 0.173 0.327
beta2_pH[7,1] 0.018 0.045 0.000 0.000 0.117
beta2_pH[8,1] 0.245 0.102 0.128 0.226 0.478
beta2_pH[9,1] 0.421 0.193 0.167 0.387 0.881
beta2_pH[10,1] 0.631 0.320 0.288 0.555 1.679
beta2_pH[11,1] 0.804 0.215 0.493 0.771 1.335
beta2_pH[12,1] 1.365 0.525 0.727 1.265 2.626
beta2_pH[13,1] 0.742 0.222 0.414 0.710 1.247
beta2_pH[14,1] 0.839 0.205 0.523 0.813 1.323
beta2_pH[15,1] 0.805 0.282 0.408 0.757 1.501
beta2_pH[16,1] 0.390 0.178 0.170 0.341 0.846
beta2_pH[1,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[2,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[3,2] -0.742 3.932 -8.270 -0.695 7.076
beta2_pH[4,2] -0.723 3.935 -8.371 -0.747 7.148
beta2_pH[5,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[6,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[7,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[8,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[9,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[10,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[11,2] -9.615 4.629 -21.313 -8.374 -3.972
beta2_pH[12,2] -8.201 5.271 -20.998 -7.179 -1.008
beta2_pH[13,2] -8.110 5.305 -21.489 -7.007 -1.660
beta2_pH[14,2] -8.717 4.993 -21.397 -7.457 -2.545
beta2_pH[15,2] -9.501 4.676 -21.310 -8.425 -3.610
beta2_pH[16,2] -9.724 4.610 -21.561 -8.637 -3.922
beta2_pH[1,3] 0.194 0.439 0.000 0.126 0.856
beta2_pH[2,3] 0.000 0.000 0.000 0.000 0.000
beta2_pH[3,3] 0.000 0.000 0.000 0.000 0.000
beta2_pH[4,3] 0.000 0.000 0.000 0.000 0.000
beta2_pH[5,3] 10.079 6.972 0.586 8.678 27.414
beta2_pH[6,3] 10.095 6.919 0.447 8.696 27.266
beta2_pH[7,3] 0.000 0.000 0.000 0.000 0.000
beta2_pH[8,3] 11.040 6.756 2.068 9.370 27.739
beta2_pH[9,3] 9.804 7.108 0.473 8.444 27.068
beta2_pH[10,3] 9.447 7.268 0.525 8.069 27.245
beta2_pH[11,3] -2.477 2.267 -9.944 -1.730 -0.611
beta2_pH[12,3] -2.605 2.149 -9.276 -1.916 -0.947
beta2_pH[13,3] -3.022 2.530 -10.661 -2.184 -0.794
beta2_pH[14,3] -2.975 2.362 -10.464 -2.166 -0.928
beta2_pH[15,3] -3.160 2.412 -10.437 -2.303 -1.031
beta2_pH[16,3] -3.179 2.488 -10.556 -2.293 -0.882
beta3_pH[1,1] 35.925 0.821 34.405 35.905 37.571
beta3_pH[2,1] 33.537 1.187 31.519 33.447 36.112
beta3_pH[3,1] 33.671 1.039 31.702 33.650 35.806
beta3_pH[4,1] 33.947 1.342 31.801 33.837 36.674
beta3_pH[5,1] 27.791 1.267 26.419 27.503 31.404
beta3_pH[6,1] 38.391 3.178 32.585 38.256 44.827
beta3_pH[7,1] 30.402 7.884 18.566 29.789 44.914
beta3_pH[8,1] 39.913 2.064 36.349 39.685 44.581
beta3_pH[9,1] 30.741 1.637 28.106 30.602 33.867
beta3_pH[10,1] 32.714 0.928 30.978 32.696 34.636
beta3_pH[11,1] 30.388 0.470 29.475 30.373 31.373
beta3_pH[12,1] 30.151 0.395 29.376 30.160 30.927
beta3_pH[13,1] 33.166 0.576 32.064 33.160 34.313
beta3_pH[14,1] 32.040 0.448 31.201 32.034 32.930
beta3_pH[15,1] 31.158 0.656 29.778 31.163 32.425
beta3_pH[16,1] 32.084 1.047 30.379 31.959 34.548
beta3_pH[1,2] 30.000 8.003 18.643 28.886 44.967
beta3_pH[2,2] 30.184 7.897 18.490 29.287 44.841
beta3_pH[3,2] 30.282 8.059 18.457 29.475 44.971
beta3_pH[4,2] 30.115 7.983 18.460 29.348 44.918
beta3_pH[5,2] 29.826 7.920 18.456 28.931 44.894
beta3_pH[6,2] 30.352 7.980 18.489 29.437 45.071
beta3_pH[7,2] 30.003 7.903 18.504 29.185 44.752
beta3_pH[8,2] 29.969 7.829 18.578 28.966 44.846
beta3_pH[9,2] 29.985 7.945 18.460 29.056 45.047
beta3_pH[10,2] 30.073 7.970 18.490 29.046 45.010
beta3_pH[11,2] 43.407 0.177 43.122 43.386 43.785
beta3_pH[12,2] 43.191 0.200 42.924 43.142 43.731
beta3_pH[13,2] 43.871 0.145 43.480 43.910 44.040
beta3_pH[14,2] 43.294 0.201 43.043 43.244 43.791
beta3_pH[15,2] 43.406 0.195 43.098 43.382 43.812
beta3_pH[16,2] 43.491 0.185 43.159 43.491 43.839
beta3_pH[1,3] 35.161 7.208 19.176 37.429 45.013
beta3_pH[2,3] 30.192 8.134 18.421 29.358 45.090
beta3_pH[3,3] 30.133 7.943 18.400 29.363 44.915
beta3_pH[4,3] 30.365 8.015 18.431 29.752 45.071
beta3_pH[5,3] 25.408 6.214 18.256 23.752 41.912
beta3_pH[6,3] 29.014 6.433 19.602 26.514 44.036
beta3_pH[7,3] 30.511 8.000 18.547 29.950 45.007
beta3_pH[8,3] 41.494 0.255 41.056 41.492 41.934
beta3_pH[9,3] 33.279 1.170 29.570 33.529 34.327
beta3_pH[10,3] 35.807 0.805 33.380 36.004 36.849
beta3_pH[11,3] 41.789 0.870 40.058 41.809 43.325
beta3_pH[12,3] 41.718 0.399 40.956 41.730 42.509
beta3_pH[13,3] 42.730 0.940 40.979 42.740 44.864
beta3_pH[14,3] 41.093 0.609 39.797 41.127 42.178
beta3_pH[15,3] 42.620 0.682 41.148 42.698 43.787
beta3_pH[16,3] 42.911 0.777 41.125 43.016 44.235
beta0_pelagic[1] 2.195 0.133 1.941 2.192 2.448
beta0_pelagic[2] 1.514 0.127 1.264 1.515 1.762
beta0_pelagic[3] 0.605 0.349 -0.375 0.716 0.991
beta0_pelagic[4] 0.863 0.331 -0.070 0.954 1.249
beta0_pelagic[5] 1.188 0.251 0.667 1.189 1.655
beta0_pelagic[6] 1.456 0.273 0.893 1.468 1.961
beta0_pelagic[7] 1.606 0.212 1.197 1.596 2.055
beta0_pelagic[8] 1.759 0.208 1.354 1.757 2.201
beta0_pelagic[9] 2.500 0.317 1.870 2.517 3.083
beta0_pelagic[10] 2.532 0.200 2.110 2.540 2.918
beta0_pelagic[11] 0.318 0.363 -0.648 0.431 0.754
beta0_pelagic[12] 1.680 0.148 1.381 1.682 1.966
beta0_pelagic[13] 0.332 0.189 -0.060 0.340 0.674
beta0_pelagic[14] -0.063 0.258 -0.628 -0.044 0.392
beta0_pelagic[15] -0.259 0.141 -0.525 -0.260 0.013
beta0_pelagic[16] 0.365 0.226 -0.239 0.401 0.686
beta1_pelagic[1] 0.000 0.000 0.000 0.000 0.000
beta1_pelagic[2] 0.000 0.000 0.000 0.000 0.000
beta1_pelagic[3] 0.291 0.565 0.000 0.000 1.893
beta1_pelagic[4] 0.204 0.430 0.000 0.000 1.424
beta1_pelagic[5] -0.076 0.312 -0.686 -0.071 0.532
beta1_pelagic[6] -0.082 0.447 -0.853 -0.113 0.754
beta1_pelagic[7] -0.018 0.291 -0.578 -0.021 0.546
beta1_pelagic[8] 0.000 0.284 -0.544 -0.004 0.570
beta1_pelagic[9] 0.184 0.491 -0.794 0.284 0.969
beta1_pelagic[10] 0.067 0.259 -0.436 0.060 0.588
beta1_pelagic[11] 3.067 0.951 2.053 2.712 5.647
beta1_pelagic[12] 2.761 0.320 2.205 2.746 3.357
beta1_pelagic[13] 2.861 0.666 1.820 2.772 4.480
beta1_pelagic[14] 4.161 0.960 2.770 3.996 6.372
beta1_pelagic[15] 2.936 0.299 2.400 2.923 3.515
beta1_pelagic[16] 3.368 0.747 2.635 3.189 5.700
beta2_pelagic[1] 0.000 0.000 0.000 0.000 0.000
beta2_pelagic[2] 0.000 0.000 0.000 0.000 0.000
beta2_pelagic[3] 0.184 0.895 0.000 0.000 1.388
beta2_pelagic[4] 0.097 0.227 0.000 0.000 0.821
beta2_pelagic[5] -0.007 0.681 -1.451 -0.007 1.417
beta2_pelagic[6] -0.075 0.680 -1.440 -0.123 1.363
beta2_pelagic[7] -0.010 0.640 -1.392 -0.004 1.314
beta2_pelagic[8] -0.004 0.643 -1.354 -0.001 1.321
beta2_pelagic[9] 0.165 0.687 -1.316 0.229 1.509
beta2_pelagic[10] -0.010 0.622 -1.422 0.004 1.294
beta2_pelagic[11] 4.085 5.388 0.133 2.190 19.757
beta2_pelagic[12] 7.165 5.621 1.133 5.454 21.785
beta2_pelagic[13] 1.006 2.478 0.206 0.488 6.301
beta2_pelagic[14] 0.339 0.147 0.169 0.302 0.732
beta2_pelagic[15] 7.169 5.377 1.323 5.617 21.960
beta2_pelagic[16] 6.427 6.189 0.235 4.945 22.741
beta3_pelagic[1] 30.040 7.951 18.566 29.011 45.128
beta3_pelagic[2] 30.211 7.970 18.535 29.356 45.147
beta3_pelagic[3] 30.328 7.476 18.580 29.552 44.767
beta3_pelagic[4] 29.610 7.642 18.518 27.874 44.888
beta3_pelagic[5] 30.242 8.252 18.483 28.759 45.177
beta3_pelagic[6] 31.915 6.793 19.050 31.832 44.475
beta3_pelagic[7] 29.798 7.912 18.462 28.880 44.792
beta3_pelagic[8] 29.294 7.936 18.465 27.752 44.558
beta3_pelagic[9] 31.135 6.293 19.220 31.200 43.363
beta3_pelagic[10] 29.528 8.296 18.322 27.974 44.851
beta3_pelagic[11] 42.910 1.273 38.970 43.141 45.073
beta3_pelagic[12] 43.470 0.285 43.023 43.457 43.953
beta3_pelagic[13] 42.814 1.250 40.417 42.817 45.469
beta3_pelagic[14] 42.206 1.603 38.971 42.227 45.357
beta3_pelagic[15] 43.226 0.244 42.730 43.205 43.742
beta3_pelagic[16] 43.215 0.590 41.734 43.236 44.609
mu_beta0_pelagic[1] 1.260 0.687 -0.314 1.291 2.567
mu_beta0_pelagic[2] 1.809 0.392 1.008 1.815 2.536
mu_beta0_pelagic[3] 0.382 0.455 -0.541 0.397 1.245
tau_beta0_pelagic[1] 1.527 1.661 0.068 0.970 6.152
tau_beta0_pelagic[2] 2.551 2.433 0.278 1.875 8.619
tau_beta0_pelagic[3] 1.693 1.265 0.197 1.401 4.962
beta0_yellow[1] -0.553 0.224 -1.053 -0.525 -0.211
beta0_yellow[2] 0.470 0.185 0.048 0.483 0.791
beta0_yellow[3] -0.340 0.214 -0.817 -0.325 0.021
beta0_yellow[4] 0.758 0.452 -0.459 0.855 1.212
beta0_yellow[5] -0.313 0.350 -1.016 -0.307 0.371
beta0_yellow[6] 1.130 0.167 0.811 1.130 1.451
beta0_yellow[7] 0.983 0.157 0.679 0.981 1.292
beta0_yellow[8] 1.016 0.158 0.711 1.016 1.329
beta0_yellow[9] 0.664 0.157 0.355 0.663 0.970
beta0_yellow[10] 0.582 0.143 0.308 0.581 0.865
beta0_yellow[11] -1.916 0.422 -2.701 -1.927 -1.065
beta0_yellow[12] -3.675 0.430 -4.590 -3.649 -2.881
beta0_yellow[13] -3.706 0.491 -4.751 -3.669 -2.845
beta0_yellow[14] -2.025 0.617 -3.078 -2.086 -0.367
beta0_yellow[15] -2.802 0.411 -3.664 -2.793 -2.019
beta0_yellow[16] -2.314 0.491 -3.185 -2.342 -1.215
beta1_yellow[1] 1.051 3.236 0.007 0.714 3.459
beta1_yellow[2] 1.162 0.466 0.608 1.079 2.538
beta1_yellow[3] 0.776 0.574 0.249 0.730 1.573
beta1_yellow[4] 1.558 1.062 0.675 1.239 4.653
beta1_yellow[5] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[6] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[7] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[8] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[9] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[10] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[11] 2.051 0.420 1.173 2.076 2.836
beta1_yellow[12] 2.463 0.445 1.658 2.430 3.409
beta1_yellow[13] 2.821 0.486 1.969 2.780 3.830
beta1_yellow[14] 2.116 0.573 0.723 2.153 3.149
beta1_yellow[15] 2.065 0.411 1.250 2.056 2.912
beta1_yellow[16] 2.070 0.490 0.979 2.092 2.954
beta2_yellow[1] -2.299 2.624 -9.967 -1.324 -0.006
beta2_yellow[2] -1.876 2.209 -8.724 -1.111 -0.140
beta2_yellow[3] -2.381 2.510 -9.278 -1.530 -0.103
beta2_yellow[4] -2.099 2.639 -9.658 -0.997 -0.072
beta2_yellow[5] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[6] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[7] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[8] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[9] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[10] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[11] -5.095 2.868 -11.611 -4.426 -1.152
beta2_yellow[12] -5.256 2.847 -12.158 -4.593 -1.393
beta2_yellow[13] -5.076 2.719 -11.780 -4.416 -1.488
beta2_yellow[14] -5.152 3.015 -12.158 -4.600 -0.601
beta2_yellow[15] -4.692 2.935 -12.034 -3.951 -1.019
beta2_yellow[16] -5.323 2.974 -12.733 -4.637 -1.369
beta3_yellow[1] 25.829 7.220 18.217 22.676 43.884
beta3_yellow[2] 29.067 2.305 22.695 29.028 33.330
beta3_yellow[3] 32.861 3.697 23.158 32.845 41.234
beta3_yellow[4] 29.162 4.019 20.693 28.172 37.109
beta3_yellow[5] 29.983 7.975 18.437 28.957 45.071
beta3_yellow[6] 30.084 7.991 18.515 29.021 44.925
beta3_yellow[7] 29.799 7.815 18.510 28.766 44.979
beta3_yellow[8] 30.234 7.981 18.452 29.436 44.934
beta3_yellow[9] 29.944 7.936 18.458 29.050 44.952
beta3_yellow[10] 30.231 8.002 18.614 29.435 44.902
beta3_yellow[11] 45.252 0.561 43.846 45.351 45.964
beta3_yellow[12] 43.301 0.378 42.500 43.287 44.039
beta3_yellow[13] 44.869 0.405 43.997 44.949 45.563
beta3_yellow[14] 43.800 2.231 34.693 44.189 45.853
beta3_yellow[15] 45.123 0.550 44.078 45.102 45.967
beta3_yellow[16] 44.507 0.890 43.293 44.532 45.853
mu_beta0_yellow[1] 0.055 0.541 -1.084 0.062 1.193
mu_beta0_yellow[2] 0.642 0.331 -0.119 0.665 1.278
mu_beta0_yellow[3] -2.380 0.659 -3.414 -2.467 -0.764
tau_beta0_yellow[1] 1.896 2.451 0.095 1.176 8.009
tau_beta0_yellow[2] 3.414 4.328 0.320 2.233 13.606
tau_beta0_yellow[3] 1.398 1.757 0.093 0.869 5.862
beta0_black[1] -0.075 0.159 -0.393 -0.076 0.236
beta0_black[2] 1.911 0.133 1.649 1.913 2.170
beta0_black[3] 1.316 0.137 1.054 1.318 1.578
beta0_black[4] 2.433 0.136 2.164 2.432 2.691
beta0_black[5] 1.550 1.915 -2.975 1.636 5.330
beta0_black[6] 1.620 1.947 -2.619 1.648 5.660
beta0_black[7] 1.604 1.922 -2.595 1.674 5.602
beta0_black[8] 1.304 0.232 0.848 1.309 1.746
beta0_black[9] 2.452 0.253 1.964 2.455 2.942
beta0_black[10] 1.474 0.140 1.211 1.473 1.746
beta0_black[11] 3.486 0.156 3.182 3.484 3.791
beta0_black[12] 4.873 0.181 4.519 4.869 5.239
beta0_black[13] -0.164 0.341 -0.878 -0.124 0.322
beta0_black[14] 2.860 0.162 2.539 2.859 3.174
beta0_black[15] 1.290 0.159 0.974 1.290 1.610
beta0_black[16] 4.278 0.165 3.954 4.275 4.613
beta2_black[1] 7.556 9.571 0.582 3.537 37.951
beta2_black[2] 0.000 0.000 0.000 0.000 0.000
beta2_black[3] 0.000 0.000 0.000 0.000 0.000
beta2_black[4] 0.000 0.000 0.000 0.000 0.000
beta2_black[5] 0.000 0.000 0.000 0.000 0.000
beta2_black[6] 0.000 0.000 0.000 0.000 0.000
beta2_black[7] 0.000 0.000 0.000 0.000 0.000
beta2_black[8] 0.000 0.000 0.000 0.000 0.000
beta2_black[9] 0.000 0.000 0.000 0.000 0.000
beta2_black[10] 0.000 0.000 0.000 0.000 0.000
beta2_black[11] 0.000 0.000 0.000 0.000 0.000
beta2_black[12] 0.000 0.000 0.000 0.000 0.000
beta2_black[13] -1.726 1.485 -5.926 -1.247 -0.147
beta2_black[14] 0.000 0.000 0.000 0.000 0.000
beta2_black[15] 0.000 0.000 0.000 0.000 0.000
beta2_black[16] 0.000 0.000 0.000 0.000 0.000
beta3_black[1] 41.793 1.027 39.884 41.944 43.298
beta3_black[2] 25.000 0.000 25.000 25.000 25.000
beta3_black[3] 25.000 0.000 25.000 25.000 25.000
beta3_black[4] 25.000 0.000 25.000 25.000 25.000
beta3_black[5] 25.000 0.000 25.000 25.000 25.000
beta3_black[6] 25.000 0.000 25.000 25.000 25.000
beta3_black[7] 25.000 0.000 25.000 25.000 25.000
beta3_black[8] 25.000 0.000 25.000 25.000 25.000
beta3_black[9] 25.000 0.000 25.000 25.000 25.000
beta3_black[10] 25.000 0.000 25.000 25.000 25.000
beta3_black[11] 25.000 0.000 25.000 25.000 25.000
beta3_black[12] 25.000 0.000 25.000 25.000 25.000
beta3_black[13] 38.881 2.097 32.926 39.253 40.592
beta3_black[14] 25.000 0.000 25.000 25.000 25.000
beta3_black[15] 25.000 0.000 25.000 25.000 25.000
beta3_black[16] 25.000 0.000 25.000 25.000 25.000
beta4_black[1] -0.256 0.195 -0.645 -0.254 0.127
beta4_black[2] 0.245 0.188 -0.115 0.245 0.608
beta4_black[3] -0.932 0.198 -1.315 -0.930 -0.536
beta4_black[4] 0.425 0.218 0.002 0.424 0.874
beta4_black[5] 0.289 2.971 -4.606 0.212 5.832
beta4_black[6] 0.225 2.588 -4.854 0.152 5.574
beta4_black[7] 0.211 2.597 -5.156 0.153 5.116
beta4_black[8] -0.703 0.388 -1.475 -0.697 0.030
beta4_black[9] 1.476 1.031 -0.131 1.335 3.842
beta4_black[10] 0.029 0.195 -0.361 0.032 0.413
beta4_black[11] -0.695 0.219 -1.118 -0.692 -0.287
beta4_black[12] 0.170 0.335 -0.463 0.162 0.850
beta4_black[13] -1.177 0.223 -1.614 -1.175 -0.750
beta4_black[14] -0.185 0.236 -0.637 -0.191 0.297
beta4_black[15] -0.886 0.219 -1.320 -0.884 -0.470
beta4_black[16] -0.587 0.232 -1.046 -0.583 -0.131
mu_beta0_black[1] 1.284 0.917 -0.678 1.300 3.141
mu_beta0_black[2] 1.603 0.865 -0.528 1.667 3.236
mu_beta0_black[3] 2.536 0.982 0.356 2.576 4.401
tau_beta0_black[1] 0.629 0.598 0.055 0.440 2.167
tau_beta0_black[2] 2.028 4.239 0.055 0.912 10.433
tau_beta0_black[3] 0.234 0.155 0.051 0.196 0.643
beta0_dsr[11] -2.887 0.295 -3.457 -2.887 -2.323
beta0_dsr[12] 4.555 0.292 4.009 4.557 5.167
beta0_dsr[13] -1.366 0.348 -2.028 -1.349 -0.767
beta0_dsr[14] -3.678 0.506 -4.688 -3.671 -2.661
beta0_dsr[15] -1.955 0.289 -2.514 -1.957 -1.375
beta0_dsr[16] -3.007 0.370 -3.745 -3.006 -2.288
beta1_dsr[11] 4.819 0.304 4.218 4.819 5.403
beta1_dsr[12] 6.317 5.616 2.219 4.933 19.291
beta1_dsr[13] 2.880 0.398 2.271 2.852 3.590
beta1_dsr[14] 6.345 0.537 5.274 6.339 7.393
beta1_dsr[15] 3.350 0.295 2.773 3.346 3.922
beta1_dsr[16] 5.826 0.385 5.067 5.824 6.583
beta2_dsr[11] -8.226 2.348 -13.751 -7.886 -4.608
beta2_dsr[12] -7.039 2.669 -12.707 -6.874 -2.315
beta2_dsr[13] -6.441 2.786 -12.338 -6.365 -1.262
beta2_dsr[14] -6.209 2.667 -11.818 -6.058 -1.836
beta2_dsr[15] -7.768 2.472 -13.601 -7.506 -3.838
beta2_dsr[16] -7.987 2.403 -13.510 -7.640 -4.315
beta3_dsr[11] 43.486 0.149 43.211 43.488 43.770
beta3_dsr[12] 33.980 0.744 32.214 34.111 34.817
beta3_dsr[13] 43.252 0.314 42.780 43.187 43.880
beta3_dsr[14] 43.347 0.235 43.073 43.276 43.931
beta3_dsr[15] 43.508 0.187 43.166 43.510 43.853
beta3_dsr[16] 43.440 0.161 43.178 43.426 43.771
beta4_dsr[11] 0.586 0.223 0.152 0.586 1.051
beta4_dsr[12] 0.234 0.440 -0.624 0.234 1.154
beta4_dsr[13] -0.165 0.226 -0.619 -0.158 0.275
beta4_dsr[14] 0.149 0.248 -0.363 0.158 0.615
beta4_dsr[15] 0.725 0.219 0.299 0.724 1.166
beta4_dsr[16] 0.157 0.234 -0.302 0.161 0.599
beta0_slope[11] -1.848 0.150 -2.146 -1.847 -1.559
beta0_slope[12] -4.473 0.263 -5.030 -4.463 -3.977
beta0_slope[13] -1.346 0.181 -1.736 -1.334 -1.016
beta0_slope[14] -2.678 0.168 -3.014 -2.673 -2.353
beta0_slope[15] -1.345 0.146 -1.634 -1.343 -1.060
beta0_slope[16] -2.738 0.159 -3.051 -2.738 -2.431
beta1_slope[11] 4.490 0.222 4.056 4.493 4.923
beta1_slope[12] 3.994 0.467 3.119 3.994 4.929
beta1_slope[13] 2.719 0.462 2.196 2.652 4.158
beta1_slope[14] 6.331 0.429 5.490 6.323 7.190
beta1_slope[15] 3.008 0.210 2.594 3.007 3.417
beta1_slope[16] 5.293 0.288 4.750 5.285 5.855
beta2_slope[11] 8.677 2.299 5.190 8.366 14.146
beta2_slope[12] 6.616 2.955 1.176 6.603 12.758
beta2_slope[13] 5.417 3.082 0.377 5.307 11.836
beta2_slope[14] 6.436 2.617 2.261 6.219 12.241
beta2_slope[15] 8.251 2.358 4.535 7.899 13.477
beta2_slope[16] 7.816 2.378 4.230 7.484 13.105
beta3_slope[11] 43.460 0.132 43.214 43.456 43.715
beta3_slope[12] 43.341 0.270 42.848 43.309 43.881
beta3_slope[13] 43.475 0.406 42.891 43.428 44.109
beta3_slope[14] 43.267 0.134 43.093 43.237 43.588
beta3_slope[15] 43.486 0.160 43.193 43.482 43.795
beta3_slope[16] 43.374 0.143 43.154 43.356 43.705
beta4_slope[11] -0.732 0.165 -1.057 -0.730 -0.415
beta4_slope[12] -1.148 0.470 -2.163 -1.106 -0.324
beta4_slope[13] 0.092 0.165 -0.229 0.091 0.420
beta4_slope[14] -0.087 0.196 -0.460 -0.094 0.298
beta4_slope[15] -0.765 0.159 -1.086 -0.764 -0.460
beta4_slope[16] -0.160 0.176 -0.503 -0.161 0.179
sigma_H[1] 0.200 0.053 0.101 0.197 0.311
sigma_H[2] 0.170 0.030 0.119 0.167 0.233
sigma_H[3] 0.195 0.042 0.119 0.192 0.283
sigma_H[4] 0.423 0.076 0.299 0.415 0.587
sigma_H[5] 0.998 0.207 0.619 0.984 1.429
sigma_H[6] 0.388 0.205 0.037 0.380 0.816
sigma_H[7] 0.310 0.066 0.208 0.301 0.467
sigma_H[8] 0.419 0.092 0.282 0.409 0.607
sigma_H[9] 0.523 0.125 0.330 0.506 0.818
sigma_H[10] 0.215 0.043 0.140 0.212 0.312
sigma_H[11] 0.277 0.045 0.202 0.273 0.373
sigma_H[12] 0.440 0.167 0.207 0.418 0.777
sigma_H[13] 0.214 0.038 0.150 0.210 0.298
sigma_H[14] 0.512 0.094 0.353 0.503 0.715
sigma_H[15] 0.248 0.041 0.179 0.244 0.337
sigma_H[16] 0.226 0.045 0.155 0.220 0.331
lambda_H[1] 2.954 3.588 0.156 1.725 12.733
lambda_H[2] 8.263 7.577 0.807 6.120 27.879
lambda_H[3] 6.215 9.245 0.253 3.109 29.392
lambda_H[4] 0.006 0.004 0.001 0.005 0.017
lambda_H[5] 3.704 7.795 0.040 1.071 25.225
lambda_H[6] 7.997 16.762 0.008 1.048 53.925
lambda_H[7] 0.013 0.009 0.002 0.010 0.036
lambda_H[8] 8.088 9.850 0.109 4.689 34.856
lambda_H[9] 0.015 0.010 0.003 0.013 0.038
lambda_H[10] 0.312 0.519 0.034 0.202 1.134
lambda_H[11] 0.267 0.457 0.011 0.124 1.300
lambda_H[12] 4.847 6.699 0.194 2.738 22.898
lambda_H[13] 3.513 3.210 0.225 2.572 11.981
lambda_H[14] 3.287 4.021 0.244 2.046 14.492
lambda_H[15] 0.030 0.131 0.004 0.016 0.108
lambda_H[16] 0.854 1.399 0.043 0.432 3.915
mu_lambda_H[1] 4.329 1.879 1.255 4.157 8.475
mu_lambda_H[2] 3.851 1.940 0.542 3.702 7.947
mu_lambda_H[3] 3.495 1.803 0.791 3.217 7.450
sigma_lambda_H[1] 8.620 4.285 2.164 7.983 18.245
sigma_lambda_H[2] 8.416 4.715 0.908 7.821 18.487
sigma_lambda_H[3] 6.233 3.944 1.013 5.384 15.871
beta_H[1,1] 6.909 1.060 4.397 7.071 8.523
beta_H[2,1] 9.884 0.503 8.832 9.909 10.785
beta_H[3,1] 7.997 0.767 6.108 8.107 9.236
beta_H[4,1] 9.152 7.957 -7.535 9.483 24.593
beta_H[5,1] 0.142 2.234 -4.397 0.242 3.994
beta_H[6,1] 3.156 4.025 -7.135 4.578 7.645
beta_H[7,1] 0.485 5.833 -11.821 0.829 11.421
beta_H[8,1] 1.399 4.427 -2.419 1.216 3.544
beta_H[9,1] 13.249 5.671 2.406 13.239 24.887
beta_H[10,1] 7.090 1.691 3.480 7.176 10.170
beta_H[11,1] 5.025 3.560 -3.367 5.646 10.002
beta_H[12,1] 2.615 1.097 0.686 2.564 4.936
beta_H[13,1] 9.008 0.947 7.117 9.092 10.485
beta_H[14,1] 2.199 1.027 0.126 2.222 4.297
beta_H[15,1] -6.041 3.856 -13.105 -6.255 2.719
beta_H[16,1] 3.475 2.700 -0.867 3.118 9.943
beta_H[1,2] 7.908 0.243 7.420 7.914 8.390
beta_H[2,2] 10.022 0.135 9.755 10.023 10.286
beta_H[3,2] 8.957 0.191 8.583 8.955 9.330
beta_H[4,2] 3.640 1.499 0.863 3.554 6.887
beta_H[5,2] 1.953 0.935 0.093 1.975 3.728
beta_H[6,2] 5.747 1.052 3.256 5.918 7.324
beta_H[7,2] 2.648 1.103 0.686 2.586 5.027
beta_H[8,2] 2.972 1.179 1.209 3.125 4.205
beta_H[9,2] 3.484 1.137 1.308 3.455 5.809
beta_H[10,2] 8.202 0.344 7.507 8.212 8.858
beta_H[11,2] 9.790 0.636 8.839 9.686 11.202
beta_H[12,2] 3.955 0.377 3.271 3.944 4.727
beta_H[13,2] 9.125 0.259 8.676 9.115 9.662
beta_H[14,2] 4.026 0.354 3.331 4.020 4.738
beta_H[15,2] 11.346 0.697 9.879 11.386 12.623
beta_H[16,2] 4.555 0.814 2.962 4.551 6.152
beta_H[1,3] 8.469 0.239 8.013 8.463 8.961
beta_H[2,3] 10.064 0.118 9.834 10.062 10.308
beta_H[3,3] 9.620 0.161 9.314 9.618 9.953
beta_H[4,3] -2.586 0.874 -4.344 -2.574 -0.878
beta_H[5,3] 3.817 0.610 2.563 3.820 5.037
beta_H[6,3] 7.996 1.198 6.349 7.613 10.651
beta_H[7,3] -2.780 0.662 -4.088 -2.770 -1.498
beta_H[8,3] 5.247 0.534 4.637 5.177 6.256
beta_H[9,3] -2.859 0.741 -4.324 -2.846 -1.456
beta_H[10,3] 8.690 0.275 8.164 8.689 9.234
beta_H[11,3] 8.523 0.293 7.909 8.544 9.052
beta_H[12,3] 5.254 0.331 4.480 5.304 5.771
beta_H[13,3] 8.842 0.173 8.493 8.851 9.167
beta_H[14,3] 5.713 0.270 5.132 5.726 6.183
beta_H[15,3] 10.371 0.318 9.764 10.366 11.010
beta_H[16,3] 6.239 0.613 4.896 6.300 7.266
beta_H[1,4] 8.259 0.176 7.882 8.265 8.577
beta_H[2,4] 10.126 0.119 9.871 10.133 10.341
beta_H[3,4] 10.123 0.164 9.755 10.139 10.410
beta_H[4,4] 11.814 0.462 10.893 11.810 12.700
beta_H[5,4] 5.476 0.745 4.308 5.377 7.212
beta_H[6,4] 7.078 0.928 4.950 7.379 8.307
beta_H[7,4] 8.275 0.348 7.584 8.275 8.933
beta_H[8,4] 6.704 0.261 6.225 6.714 7.130
beta_H[9,4] 7.212 0.480 6.254 7.214 8.135
beta_H[10,4] 7.750 0.234 7.309 7.741 8.242
beta_H[11,4] 9.393 0.197 8.998 9.393 9.771
beta_H[12,4] 7.150 0.219 6.742 7.138 7.598
beta_H[13,4] 9.048 0.141 8.760 9.054 9.317
beta_H[14,4] 7.722 0.217 7.305 7.720 8.148
beta_H[15,4] 9.469 0.236 8.975 9.471 9.936
beta_H[16,4] 9.340 0.244 8.911 9.330 9.847
beta_H[1,5] 8.988 0.141 8.698 8.992 9.257
beta_H[2,5] 10.780 0.092 10.607 10.776 10.967
beta_H[3,5] 10.926 0.172 10.615 10.917 11.287
beta_H[4,5] 8.382 0.472 7.494 8.371 9.336
beta_H[5,5] 5.435 0.554 4.186 5.471 6.415
beta_H[6,5] 8.797 0.624 7.921 8.638 10.313
beta_H[7,5] 6.755 0.343 6.080 6.752 7.416
beta_H[8,5] 8.213 0.218 7.846 8.199 8.652
beta_H[9,5] 8.204 0.479 7.259 8.207 9.153
beta_H[10,5] 10.085 0.228 9.635 10.086 10.532
beta_H[11,5] 11.508 0.226 11.070 11.508 11.937
beta_H[12,5] 8.490 0.203 8.094 8.482 8.905
beta_H[13,5] 10.012 0.129 9.763 10.010 10.267
beta_H[14,5] 9.195 0.232 8.777 9.185 9.684
beta_H[15,5] 11.164 0.247 10.690 11.160 11.661
beta_H[16,5] 9.918 0.176 9.555 9.924 10.249
beta_H[1,6] 10.179 0.181 9.863 10.167 10.570
beta_H[2,6] 11.513 0.105 11.296 11.516 11.717
beta_H[3,6] 10.806 0.165 10.451 10.819 11.098
beta_H[4,6] 12.877 0.828 11.179 12.897 14.428
beta_H[5,6] 5.873 0.586 4.756 5.867 7.090
beta_H[6,6] 8.769 0.692 6.936 8.908 9.736
beta_H[7,6] 9.863 0.574 8.759 9.866 10.985
beta_H[8,6] 9.513 0.294 8.978 9.536 9.959
beta_H[9,6] 8.471 0.774 6.986 8.458 10.025
beta_H[10,6] 9.518 0.317 8.814 9.549 10.069
beta_H[11,6] 10.814 0.349 10.070 10.839 11.432
beta_H[12,6] 9.375 0.257 8.876 9.370 9.913
beta_H[13,6] 11.050 0.166 10.756 11.041 11.397
beta_H[14,6] 9.823 0.290 9.232 9.833 10.383
beta_H[15,6] 10.840 0.430 9.968 10.845 11.642
beta_H[16,6] 10.533 0.246 10.020 10.540 10.996
beta_H[1,7] 10.892 0.832 8.874 10.986 12.246
beta_H[2,7] 12.220 0.431 11.333 12.222 13.069
beta_H[3,7] 10.561 0.655 9.106 10.629 11.663
beta_H[4,7] 2.510 4.243 -5.522 2.398 11.269
beta_H[5,7] 6.418 1.703 3.058 6.390 10.097
beta_H[6,7] 9.649 2.522 4.700 9.563 15.942
beta_H[7,7] 10.532 2.912 4.822 10.531 16.215
beta_H[8,7] 10.961 1.104 9.390 10.892 12.797
beta_H[9,7] 4.425 3.950 -3.676 4.512 12.353
beta_H[10,7] 9.808 1.469 7.192 9.735 13.051
beta_H[11,7] 10.962 1.698 7.799 10.852 14.716
beta_H[12,7] 9.980 0.960 7.962 10.056 11.631
beta_H[13,7] 11.651 0.774 9.818 11.748 12.877
beta_H[14,7] 10.392 0.923 8.348 10.438 12.072
beta_H[15,7] 12.022 2.231 7.739 11.952 16.519
beta_H[16,7] 12.272 1.300 10.086 12.098 15.208
beta0_H[1] 8.699 13.669 -18.479 8.839 34.055
beta0_H[2] 10.608 6.350 -1.752 10.751 22.861
beta0_H[3] 9.757 10.330 -10.757 9.812 29.803
beta0_H[4] 8.903 190.372 -403.584 8.030 383.009
beta0_H[5] 4.905 22.949 -40.526 4.716 51.571
beta0_H[6] 6.939 50.675 -106.233 7.586 115.058
beta0_H[7] 8.483 138.815 -282.806 9.944 279.084
beta0_H[8] 6.608 37.925 -14.591 6.522 30.949
beta0_H[9] 7.194 131.461 -238.046 8.713 258.851
beta0_H[10] 8.918 32.532 -57.709 8.217 78.013
beta0_H[11] 9.027 50.020 -99.310 9.319 113.962
beta0_H[12] 6.903 12.103 -16.565 6.926 29.799
beta0_H[13] 9.417 10.691 -12.227 9.653 28.512
beta0_H[14] 6.867 11.361 -16.468 7.170 29.472
beta0_H[15] 6.712 106.878 -216.043 7.218 220.558
beta0_H[16] 7.474 25.394 -45.178 7.856 56.084